Interval estimation of variance ratio in non-normal unbalanced one-way random models

Abstract

Confidence intervals based on the harmonic mean method are proposed for estimating the ratio of variance components and/or the intraclass correlation coefficient (ρ) in unbalanced one-way random models without the normality assumptions. Since the proposed procedure is heavily dependent on the estimation of the kurtosis of the underlying distributions, bias-corrected estimators of kurtosis are proposed as well. Several asymptotic results concerning the proposed procedure are given along with simulation results to assess its performance in finite sample size situations. The proposed intervals are also compared with the corresponding confidence intervals based on the arithmetic mean method and were found to effectively maintain the nominal probability of coverage, except for leptokurtic distributions with fairly large kurtosis where the intervals tend to be liberal. According to the simulation results, the proposed harmonic mean intervals are recommended for use in practice. However, while computing the harmonic mean intervals, the bias-corrected estimators of kurtosis should be used when it is anticipated that ρ is small, but for large ρ the empirically corrected estimators of kurtosis should be adopted. The procedure is illustrated using a real data set.

Keywords:

• interval estimation
• intraclass correlation
• harmonic mean method
• kurtosis estimation
• unbalanced mixed models
• variance components

AMS Subject Classifications:

• 62K05
• 62F25
• 62J99

Acknowledgements

The authors thank two anonymous referees and the Associate Editor for their constructive comments which have significantly improved the quality of the paper. The research of Dr El-Bassiouni was funded by the Summer Research Grant Program of the Faculty of Business and Economics, UAE University.